chapter
POWER COMPARISONS FOR UNIVARIATE TESTS FOR NORMALITY
Pages 16

The most frequent measure of the value of a test for normality is its power, the ability to detect when a sample comes from a non-normal distribution. All else being equal (which decidedly never happens) the test of choice is the most powerful. However, in addition to power which depends on both the alternative distribution and sample size, choice of test when assessing normality can be based on a variety of other reasons, including ease of computation and availability of critical values. Ideally, one would prefer the most powerful test for all situations, while in reality no such test exists.

Often, while the specific alternative is not known, some general characteristics of the data may be known in advance (e.g., skewness). If not, there may be limited concerns about the types of departures from normality. For example, regression residuals which are symmetric but have short tails are